Question

the scores on a test are normally distributed with a mean of 40 and a standard deviation of 8. find the score that is two and one - half standard deviations below the mean. a score of is two and one - half standard deviations below the mean

Explanation:

Step1: Identify the formula

The formula for a value \(x\) in a normal distribution is \(x=\mu + z\sigma\), where \(\mu\) is the mean, \(z\) is the number of standard deviations, and \(\sigma\) is the standard deviation. Here, \(\mu = 40\), \(\sigma=8\), and \(z=- 2.5\) (since it is below the mean).

Step2: Substitute the values into the formula

Substitute the values into \(x=\mu + z\sigma\):

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Answer:

\(20\)